//Group G is generated by
//c2c5(1 4)
//c1c4(1 5 4)
//c2c3(2 3)
//c2c3


3.C3:D4
MatrixGroup(11, Integer Ring) of order 2^3 * 3
Generators:

    c2c5(1 4)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  0  0  1  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [-1  0  0 -1  0  0  0  0  0  0  0]
    [ 0  0  0  0  1  0  0  0  0  0  0]
    [ 0  0  1  0  0  0  0  0  0  0  0]
    [-1  0  0  0  0  0 -1  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    c1c4(1 5 4)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  1  0  0  0  1  0  0  0  0]
    [-1  0  0  0  0  0 -1  0  0  0  0]
    [ 0  0  0  1  0  0  0  0  0  0  0]
    [ 0  0  0  0  1  0  0  0  0  0  0]
    [-1  0 -1  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    c2c3(2 3)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  1  0  0  0  0  0  0]
    [ 0  0  1  0  0  0  0  0  0  0  0]
    [-1  0  0  0 -1  0  0  0  0  0  0]
    [-1  0  0 -1  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  1  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]
    
    c2c3
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  1  0  0  0  0  0  0]
    [ 0  0  1  0  0  0  0  0  0  0  0]
    [-1  0  0 -1  0  0  0  0  0  0  0]
    [-1  0  0  0 -1  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  1  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]
1
{@
    Mod: ( 0  1 -1  0  0  0  0  0  0  0  0),
    Mod: ( 0  1  0  0  0  0 -1  0  0  0  0),
    Mod: (0 0 0 0 0 0 1 0 0 0 0),
    Mod: (0 0 1 0 0 0 0 0 0 0 0),
    Mod: ( 0  1  0  0  0 -1  0  0  0  0  0),
    Mod: (0 0 0 0 0 1 0 0 0 0 0)
@}
Intersection Matrix:
[-1  0  0  1  0  0]
[ 0 -1  1  0  0  0]
[ 0  1 -1  0  0  0]
[ 1  0  0 -1  0  0]
[ 0  0  0  0 -1  1]
[ 0  0  0  0  1 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(11, Integer Ring)
Generators:
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  1  0  0  0  0  0  0]
    [ 0  0  1  0  0  0  0  0  0  0  0]
    [-1  0  0 -1  0  0  0  0  0  0  0]
    [-1  0  0  0 -1  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  1  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  1  0  0  0  0  0  0]
    [ 0  0  1  0  0  0  0  0  0  0  0]
    [-1  0  0  0 -1  0  0  0  0  0  0]
    [-1  0  0 -1  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  1  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    [1 0 0 0 0 0 0 0 0 0 0]
    [0 1 0 0 0 0 0 0 0 0 0]
    [0 0 1 0 0 0 0 0 0 0 0]
    [0 0 0 0 1 0 0 0 0 0 0]
    [0 0 0 1 0 0 0 0 0 0 0]
    [0 0 0 0 0 1 0 0 0 0 0]
    [0 0 0 0 0 0 1 0 0 0 0]
    [0 0 0 0 0 0 0 1 0 0 0]
    [0 0 0 0 0 0 0 0 1 0 0]
    [0 0 0 0 0 0 0 0 0 1 0]
    [0 0 0 0 0 0 0 0 0 0 1]
2
{@
    Mod: (0 0 0 1 0 0 0 0 0 0 0),
    Mod: (0 0 0 0 1 0 0 0 0 0 0),
    Mod: ( 0  1  0  0 -1  0  0  0  0  0  0),
    Mod: ( 0  1  0 -1  0  0  0  0  0  0  0)
@}
Intersection Matrix:
[-1  0  0  1]
[ 0 -1  1  0]
[ 0  1 -1  0]
[ 1  0  0 -1]
Stabilizer Group Name:
S3
MatrixGroup(11, Integer Ring)
Generators:
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  0  1  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  1  0  0  0  0]
    [ 0  0  0  1  0  0  0  0  0  0  0]
    [-1  0  0  0 -1  0  0  0  0  0  0]
    [-1  0  0  0  0 -1  0  0  0  0  0]
    [ 0  0  1  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  1  0  0  0  1  0  0  0  0]
    [-1  0  0  0  0  0 -1  0  0  0  0]
    [ 0  0  0  1  0  0  0  0  0  0  0]
    [ 0  0  0  0  1  0  0  0  0  0  0]
    [-1  0 -1  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]